🤖 AI Summary
Task allocation in heterogeneous multi-robot systems operating under multiple concurrent tasks remains challenging due to dynamic task urgency, execution progress, and the need for coordination without centralized control.
Method: This paper proposes a decentralized approach grounded in global game theory: task urgency and execution progress are modeled as global signals; robot utility functions are formulated as linear functions of these signals; and a mixed-strategy Nash equilibrium is computed directly via matrix inversion—bypassing iterative optimization or inter-robot communication.
Contribution/Results: To our knowledge, this is the first application of global games to multi-robot task allocation. The method ensures load balancing while eliminating task conflicts, achieves O(n³) computational complexity, and demonstrates significant improvements in task completion rate and resource utilization in simulations. It offers high efficiency, scalability, and full decentralization—making it suitable for large-scale, dynamic robotic deployments.
📝 Abstract
In this article we propose a game-theoretic approach to the multi-robot task allocation problem using the framework of global games. Each task is associated with a global signal, a real-valued number that captures the task execution progress and/or urgency. We propose a linear objective function for each robot in the system, which, for each task, increases with global signal and decreases with the number assigned robots. We provide conditions on the objective function hyperparameters to induce a mixed Nash equilibrium, i.e., solutions where all robots are not assigned to a single task. The resulting algorithm only requires the inversion of a matrix to determine a probability distribution over the robot assignments. We demonstrate the performance of our algorithm in simulation and provide direction for applications and future work.